demo_newton_3D.py

# -*- coding: utf8 -*-
# This file runs the restricted shape Newton method with a 3D mesh
# and 1 mesh refinement.
#
# Designed for FEniCS 2018.1.

# Import the class for the Newton method
from RestrictedShapeNewtonMethod import *

# Do not bother us with many messages
set_log_level(LogLevel.WARNING)
import logging
logging.getLogger('FFC').setLevel(logging.WARNING)

# Create a 3D box mesh 
meshlevel = 2
mesh = BoxMesh(Point(-0.5,-0.5,-0.5), Point(0.5,0.5,0.5), meshlevel, meshlevel, meshlevel)
mesh = refine(mesh)

# Set the rhs for the PDE
rhs = "Constant(2.5)*(x + Constant(0.4) - y**2)**2 + x**2 + y**2 + z**2 - Constant(1.0)"

# Generate an instance of shape optimization problem in 3D and solve it
# using the novel restricted Newton method, then refine the mesh, and run again
problem = RestrictedShapeNewtonMethod(mesh = Mesh(mesh), rhs = rhs, JSONinput = "input_newton_3D.json")
problem.run()
refinements = 1
for i in range(refinements):
	problem.mesh = refine(problem.mesh)
	problem.run()